I just ran the microwave on our 4000 watt Magnum inverter for 2 minutes which heated up a cup of water to boiling (actual bubbles popping).
Specs:
2x125AH 12V Lifeline AGM
4000 watt 24V input MSH4024M inverter
Microwave panel spec (input 1050 watts, output 700 watts)
While running, the Magnum panel said the voltage it was seeing was 24.2V and the current from the batteries was 58 amps. So total of 1400 watts. Hmmm, not super efficient if the microwave is really only drawing 1050 watts but maybe that is suspect. Efficiency would be 75%.
Anyway, at 58 amps the 125 amp-hour batteries would be down to 50% capacity in less than an hour (would have to figure from the Peukert plots), probably something like 30 min to 50%.
So for a small 2 battery system (but big inverter!) probably should limit the microwave to shore power or only use during the day when 1000 watts of solar is dumping into the battery system.